This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.
White Noise and Its Probability Distribution; Linear Functionals of White Noise; Gaussian Systems and Their Representations; Nonlinear Functionals of White Noise; Hida Distributions (Generalized Functionals of White Noise); Applications to Quantum Dynamics, Statistics and Biology.